Is there a word that can be used to refer to a collection of "donations" or "payments"?
Solution 1:
Consider funding
Providing financial resources to finance a need, program, or project. In general, this term is used when a firm fills the need for cash from its own internal reserves, and the term 'financing' is used when the need is filled from external or borrowed money.
Or simply fund
an amount of money that is used for a special purpose available money : an amount of something that is available for use : a supply of something
You could say "I created this fund to accept donations/payments for X"
Also consider pool
A fund containing all the money bet in a game of chance or on the outcome of an event.
"big public investment pools"
Solution 2:
To me, 'campaign' suggests something that has a limited life, like a run for president, a kickstarter project, etc - basically anything that at one point stops collecting funds (making funding in this context a rather ambiguous phrase to use as well, assuming the TS is not talking about long term product R&D).
Services and products are often longer-run endeavours, so with these differences clear, I am not sure if there is one word that can cover both scenarios without going so high level it's not intuitive anymore (there's bees, and flies and both are insects - there's campaigns and product launches, both can be considered to be undertakings..but it doesn't really say anything).
Personally, to avoid ambiguous wording that possibly lead to false expectations, advertising, law suits, etc, I would opt to have the organisation (at least in the back end) select one of the 2 systems in place: 'Create donation based project' and 'Create payment based project', where the first is where visitors can make a donation and not expect anything in return and the second where visitors can actually order a product/service.
Solution 3:
How about drive?
A strong organized effort to accomplish a purpose: a drive to finish the project before the deadline; fund-raising drive FOD
An effort made by a group of people to achieve a goal, to collect money, etc. M-W
Solution 4:
You could consider using "fund account". Account means:
a record of debit and credit entries to cover transactions involving a particular item or a particular person or concern
[Merriam-Webster]
Your example:
To be more specific, a fund account can be created by an organization to...
If you use "a fund account for donation and payment", it would be more clear, but I don't see any problem using just a fund account.